Dynamic Column Generation for Dynamic Vehicle Routing with Time Windows

We consider a dynamic vehicle routing problem with hard time windows, in which a set of customer orders arrives randomly over time to be picked up within their time windows. The dispatcher does not have any deterministic or probabilistic information on the location and size of a customer order until it arrives. The objective is to minimize the sum of the total distance of the routes used to cover all the orders. We propose a column-generation-based dynamic approach for the problem. The approach generates single-vehicle trips (i.e., columns) over time in a real-time fashion by utilizing existing columns, and solves at each decision epoch a set-partitioning-type formulation of the static problem consisting of the columns generated up to this time point. We evaluate the performance of our approach by comparing it to an insertion-based heuristic and an approach similar to ours, but without computational time limit for handling the static problem at each decision epoch. Computational results on various test problems generalized from a set of static benchmark problems in the literature show that our approach outperforms the insertion-based heuristic on most test problems.